President George W. Bush and Palestinian Authority President Mahmoud Abbas agreed in a telephone conversation Tuesday that if any new cease-fire agreement is to be effective in the Mideast, "it must be respected by Hamas," the White House said. Briefing reporters at Bush's Texas ranch, spokesman Gordon Johndroe reiterated the U.S. call for the militant Hamas organization to stop firing rockets into Israel. He said that Bush talked to both Abbas and Prime Minister Salam Fayed after having a briefing by videoconference with his own top aides on the fast-paced developments in Gaza. He said that Fayed thanked the United States for an $85 million contributions that it made this week to a special United Nations fund to assist Palestinians in both Gaza and the West Bank and said that Bush also called Egyptian President Hosni Mubarak to thank him for his peacemaking role there. Johndroe said that "for any cease-fire to be effective, it must be respected by Hamas." Bush's spokesman added that in the absence of such a stance, a cease-fire agreement wouldn't be worth the "paper that it's written on." He also said that Secretary of State Condoleezza Rice and national security adviser Stephen Hadley had been in touch with Israeli Prime Minister Ehud Olmert and his staff. Bush, who has not spoken with Olmert since before the crisis, was expected to talk with the Israeli leader soon, Johndroe said later. Bush, Johndroe said, told both Abbas and Fayyad that the United States was concerned about the humanitarian situation. "The president is concerned about the citizens of Gaza," he said, "but not the Hamas terrorist leaders." "The only way that this is going to stop is if Hamas stops firing missiles" and all sides agree to a sustainable cease-fire, he added. "Hopefully they (Hamas) will see the light and serve the people of Gaza," Johndroe said. Earlier, the State Department said that Rice was keeping up steady U.S. calls for a "durable and sustainable" _ but not necessarily immediate _ cease-fire to end Israel's assault on Gaza and rocket attacks by Palestinian militants based there. In phone calls with Israeli and Arab leaders, including Jordan's King Abdullah II, as well as other interested regional and international officials, spokesman Gordon Duguid said, she pressed for durable solution to the fighting that is not used by the radical Hamas movement to launch more attacks into Israel, the State Department said. "She is working extremely hard to try and get both sides to agree that a cease-fire can be re-established and that that cease-fire can be fully respected," Duguid told reporters. Others have called for an "immediate" halt to the violence, but Duguid refused to use that term, calling instead for a "durable and sustainable" cease-fire that produces "lasting peace." "The cease-fire, in order to be productive, has to be maintained," he said. "It can't be a cease-fire in which one side uses it to launch periodic attacks." Rice called King Abdullah on Tuesday. On Monday, she spoke Israeli Prime Minister Ehud Olmert and Foreign Minister Tzipi Livni as well as the foreign ministers of Egypt, Saudi Arabia and the United Arab Emirates. In the past 24 hours, Rice has also been in touch with her British counterpart, David Miliband, and European Union foreign policy chief Javier Solana twice each, along with Russian Foreign Minister Sergey Lavrov. In addition to Rice's telephone talks with individuals, she also held a conference call with other members of the international Quartet of Mideast peacemakers, the State Department said. The group includes the foreign ministers of the United States and Russia, European Union foreign policy chiefs and UN Secretary General Ban Ki-moon. "Secretary Rice continued to intensify her diplomatic efforts on the crisis in Gaza today," Duguid said. "She held a lengthy discussion with her Quartet counterparts and continues to engage a number of leaders in the Middle East." The department also formally announced the $85 million contribution for Palestinians in Gaza and the West Bank and urged "all concerned" to allow aid workers to distribute supplies. "We call on all concerned to protect innocent lives and to address the urgent humanitarian needs of the people of Gaza, by facilitating necessary access into Gaza for (the UN) and other humanitarian organizations," it said in a statement.